54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the Chain Rule. (b) by using a property of logarithms and differentiating.

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: 2. g'(x) where g(x)= x² +7x-5

A: differentiation by using first principle

Q: Solve for the 4th derivative of function K K= x3Cos√x

A:

Q: 1. Find the derivative of each of the following functions using chain rule: y=3x* (x* -2) a)

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Q: (14) Use log differentiation to find the derivative of the function. Y = (sin (7x))*

A: Here, the given function is: y=(sin(7x))x Taking logarithm on both sides, we have: ln y=ln(sin(7x))x…

Q: ex = cosy

A:

Q: y = ln 1-x² 1+x²

A:

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: Find the first order derivative with respect to y of the function u = log(x + x² – y2)

A: Using derivatives.

Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: Determine the first derivative of the ff. function y = ln| le* – 1/

A: We have to find the first derivative of the function: y=lnexex-1 We know the property of logarithm,…

Q: need fast

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Q: y = In- e 2x+1

A:

Q: 3 7 - use logarithm differentiation to differentiate to find y prime (dy). y = x

A: The given function is, y = x.Take log on both sides of the function.

Q: II. Determine the derivative of the ff. logarithmic functions 7. y = 12x² log 8x 8. y = In 25x %3D…

A: Solution is below

Q: Find the first derivative of the following functions with respect to x y = In(ln(In x))

A: To find first derivative of the given function.

Q: Q1: Find the derivative of the functions. 5- y = (csche)(1- In csche) 6- y = log3 (1 + 0 In 3) %3D

A: 5. y=cschθ1-ln cschθ6. y=log31+θ ln3

Q: In (In e*1): What is the derivative of y 3z²+1

A:

Q: 4. Find the derivative of the following function 1 y = xtanx + -

A:

Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

Q: compute a formula for the nth derivative of f(x)=e2x

A: We have givenWe have to find a formula for nth derivative of f(x)

Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

A:

Q: Find the nth derivative of the function y=ln(ax+b).

A: Given function is Differentiating with respect to x repeatedly, we get In general,

Q: Verify that the derivative and integral results for a general base b reduce to the expected results…

A: Note that ddxbux=lnbeuxu'x,∫bxdx=bxlnb+C.

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x? +…

A: Given is the function y=log(x2+1)2   .  It is needed to compute backward difference approximation…

Q: Find the derivative of the following function. y= 4 ln x – In(x-8)

A: we have to derivative

Q: Find the derivative of the function. Y= q56* In(2)ln(5)ln(6)· 3*. 5".; 2:56*+1+x

A: Given problem:-

Q: 3. Find the derivative of the following using logarithmic differentiation: 2x a. y = (2x – 1)(x + 1)…

A: To find the derivative by using logarithmic differentiation first take  the  logarithm on  both…

Q: 3// By using logarithmic differentiation and with respect to independent variable x, find the…

A:

Q: Find the derivative of y with respect to x. y=log(base)5 e^7x

A:

Q: 4) Find the derivative of each function. a. f (x) = In(x² – 4) In e c. f (x) = b. f (x) = x² ln x

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Q: Determine the derivative: y = log (3x2) (01)प य log (3) ** In(10) 6 log (Sx) r In(10) Oy= 18x In(10)…

A:

Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: Compute backward difference approximations for the first derivative of the function, y = log(x² +…

A: We have to compute backward difference approximations for the first derivative of the function,…

Q: find the derivative of y with respect to the givenindependent variable. y = log2 5θ

A:

Q: 2. Find derivative of given function defined as follows 2x y = e = ²

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: Find the derivative of the function. y = log 6 V3x+7 3. O A. In 6 3 In 6 O B. 3x +7 In 6 (3x + 7) 3…

A: Given, y = log63x + 7Applying the log rule; logab = lnblnay = ln3x + 7ln6Differentiating with…

Q: 4. Show that the derivative of log,(Va +5) is 3(r + 5) In(2)

A:

Q: 11.Find the derivative of the functions: a) f(x) = In(9x²2 – 3x) b) g(x) = In(ln x)

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Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

A:

Q: 24. Find the first order derivative with respect to x of the function u = log(x+ x .

A: The solution for the above question is as shown below.

Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10

Q: Find the anti-derivative of g'(x)= log1/2(X)

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Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

A:

Q: Monday, 1) Find the derivative of the given function with respects to e y = 3lan® In 3

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Q: find the derivative of y with respect to the givenindependent variable. y = log3 (1 + θ ln 3)

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Q: dy Y= x ²x-> メ =人

A:

Q: 1- Find the first derivative of y with respect to x for the following functions: In5 7x y = log5 . a…

A: